[1]} give asymptotics for the Cut model. Because \(\delta \) -SMI is a kind of Cut-model inference (recall, the observation model \(p_\delta (Y|\varphi ,\tilde{\theta })\)  is normalised) that theory applies here. Denote by
\((\varphi ^*_\delta ,\tilde{\theta }^*_\delta )&=\arg \max _{\varphi ,\tilde{\theta }}E_{p^*(y,z)}(p(z|\varphi )p_\delta (y|\varphi ,\tilde{\theta }))\\\theta ^*_\delta &=\arg \max _{\theta }E_{p^*(y)}(p(y|\varphi ^*_\delta ,\theta ))\) 
